When do you know whether to use "vážíme" or "respectujeme"?
You can use either. Respektovat can be forced by subordination. Vážit si is some real honest respect.
Ah, I see. Thank you!
Is there any other ways to use vážít as respect someone?
How other? It must be the reflexive "vážit si".
I'm asking because I've seen vážit used as weighting or respecting.
Yes, vážit is used for weighing. But the verb here -- vážit SI -- is used for respecting and appreciating.
Why isn't "My si vážíme tvojí ženy" accepted?
It was missing. Please use the report button "My answer should have been accepted". Reports in the discussion can be removed at any time.